Perfect gas convection in a porous medium between two coaxial horizontal cylinders of large length

Natural convection of a perfect gas in a porous medium between two coaxial horizontal cylinders of large length located in heat-conducting space is considered. The two-dimensional problem (thin porous ring) is investigated in a plane orthogonal of the axis of the cylinders. The dependence of the criterion of the onset of convection on the non-Boussinesq parameters is studied. In the steady-state case an analytic solution of the nonlinear problem is obtained and its asymptotic behavior is considered for large Rayleigh numbers and when the compressibility criterion tends to zero. The gas flow rate in the ring and other characteristics of convection are studied as functions of the gas compressibility criterion and a constant temperature gradient given far away from the contour.